Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

2014 GO423 Symposium

The Game On program and the Game On Symposium supports sector building and sustainability of the local game making industry through strengthening community networks and fostering recognition of our local game making industry. The Game On Symposium – GO423 is a two-day festival focused on Queensland practitioners and community – from leaders in the field to emerging professionals and students (High School and tertiary level). With a program of presentations, debates, discussions, and exhibition around interactive screen culture and practice, GO423 promotes an understanding of the Queensland and Australian screen production industry within a broad global context.

Mesenchymal stromal cells transiently alter the inflammatory milieu post-transplant to delay graft-versus-host disease

Background: Multipotent mesenchymal stromal cells suppress T-cell function in vitro, a property that has underpinned their use in treating clinical steroid-refractory graft-versus-host disease after allogeneic hematopoietic stem cell transplantation. However the potential of mesenchymal stromal cells to resolve graft-versus-host disease is confounded by a paucity of pre-clinical data delineating their immunomodulatory effects in vivo. Design and Methods: We examined the influence of timing and dose of donor-derived mesenchymal stromal cells on the kinetics of graft-versus-host disease in two murine models of graft-versus-host disease (major histocompatibility complex-mismatched: UBI-GFP/BL6 [H-2b]→BALB/c [H-2d] and the sibling transplant mimic, UBI-GFP/BL6 [H-2b]→BALB.B [H-2b]) using clinically relevant conditioning regimens. We also examined the effect of mesenchymal stromal cell infusion on bone marrow and spleen cellular composition and cytokine secretion in transplant recipients. Results: Despite T-cell suppression in vitro, mesenchymal stromal cells delayed but did not prevent graft-versus-host disease in the major histocompatibility complex-mismatched model. In the sibling transplant model, however, 30% of mesenchymal stromal cell-treated mice did not develop graft-versus-host disease. The timing of administration and dose of the mesenchymal stromal cells influenced their effectiveness in attenuating graft-versus-host disease, such that a low dose of mesenchymal stromal cells administered early was more effective than a high dose of mesenchymal stromal cells given late. Compared to control-treated mice, mesenchymal stromal cell-treated mice had significant reductions in serum and splenic interferon-γ, an important mediator of graft-versus-host disease. Conclusions: Mesenchymal stromal cells appear to delay death from graft-versus-host disease by transiently altering the inflammatory milieu and reducing levels of interferon-γ. Our data suggest that both the timing of infusion and the dose of mesenchymal stromal cells likely influence these cells’ effectiveness in attenuating graft-versus-host disease.

Reduced intensity conditioning for allogeneic hematopoietic stem cell transplant determines the kinetics of acute Graft-Versus-Host Disease

Background Preparative myeloablative conditioning regimens for allogeneic hematopoietic stem-cell transplantation (HSCT) may control malignancy and facilitate engraftment but also contribute to transplant related mortality, cytokine release, and acute graft-versus-host disease (GVHD). Reduced intensity conditioning (RIC) regimens have decreased transplant related mortality but the incidence of acute GVHD, while delayed, remains unchanged. There are currently no in vivo allogeneic models of RIC HSCT, limiting studies into the mechanism behind RIC-associated GVHD. Methods We developed two RIC HSCT models that result in delayed onset GVHD (major histocompatibility complex mismatched (UBI-GFP/BL6 [H-2b]→BALB/c [H-2d]) and major histocompatibility complex matched, minor histocompatibility mismatched (UBI-GFP/BL6 [H-2b]→BALB.B [H-2b])) enabling the effect of RIC on chimerism, dendritic cell (DC) chimerism, and GVHD to be investigated. Results In contrast with myeloablative conditioning, we observed that RIC-associated delayed-onset GVHD is characterized by low production of tumor necrosis factor-α, maintenance of host DC, phenotypic DC activation, increased T-regulatory cell numbers, and a delayed emergence of activated donor DC. Furthermore, changes to the peritransplant milieu in the recipient after RIC lead to the altered activation of DC and the induction of T-regulatory responses. Reduced intensity conditioning recipients suffer less early damage to GVHD target organs. However, as donor cells engraft, activated donor DC and rising levels of tumor necrosis factor-α are associated with a later onset of severe GVHD. Conclusions Delineating the mechanisms underlying delayed onset GVHD in RIC HSCT recipients is vital to improve the prediction of disease onset and allow more targeted interventions for acute GVHD.

Cube Jam (Engagement Innovation Project)

Cube Jam is a project developed in response to the new and rising marketing in large-scale interactive public screens - the Cube being a premier site. Cube Jam will be a crossbreeding ‘think-ubator’ that rides on the back of the already nationally recognised Game On program and its digital communities. Via a bottom-up, non-directive approach Cube Jam will facilitate a series of design provocations within co-located Jam Studios; studios that are focused on supporting adaptation and new ideation and concept design. These Studios will seek new combinations of skills and knowledges with the intention of discovering provotypes of possibilities in both working and production methodologies and product outcomes.

Differences in composition of symptom clusters between older and younger oncology patients

Context Older oncology patients have unique needs associated with the many physical, psychological,and social changes associated with the aging process. The mechanisms underpinning and the impact of these changes are not well understood. Identification of clusters of symptoms is one approach that has been used to elicit hypotheses about the biological and/or psychological basis for variations in symptom experiences. Objectives The purposes of this study were to identify and compare symptom clusters in younger (<60 years) and older ($60 years) patients undergoing cancer treatment. Methods. Symptom data from one Australian study and two U.S. studies were combined to conduct this analysis. A total of 593 patients receiving active treatment were dichotomized into younger (<60 years) and older ($60 years) groups. Separate exploratory factor analyses (EFAs) were undertaken within each group to identify symptom clusters from occurrence ratings of the 32 symptoms assessed by the Memorial Symptom Assessment Scale. Results In both groups, a seven-factor solution was selected. Four partially concordant symptom clusters emerged in both groups (i.e., mood/cognitive, malaise, body image, and genitourinary). In the older patients, the three unique clusters reflected physiological changes associated with aging, whereas in the younger group the three unique clusters reflected treatment-related effects. Conclusion The symptom clusters identified in older patients typically included a larger and more diverse range of physical and psychological symptoms. Differences also may be reflective of variations in treatment approaches between age groups. Findings highlight the need for better understanding of variation in treatment and symptom burden between younger and older adults with cancer.